An automobile moves under the action of a constant power supplied by its engine ,it follows that

Options

A. The driving roce and velocity ,both are constant
B. The driving force is constant but not the velocity
C. The velocity is constant but not the driving force
D. Both driving force as well as velocity vary

Explanation

To solve the problem, we need to analyze the relationship between power, force, and velocity in the context of an automobile moving under the action of constant power.

### Step-by-Step Solution:

1. **Understanding Power**:
Power (P) is defined as the rate at which work is done or energy is transferred. In the context of an automobile, the power supplied by the engine is given by the equation:
\[ P = F \cdot v \]
where \( F \) is the driving force and \( v \) is the velocity of the automobile.

2. **Constant Power**:
Since the power is constant, we can express this as:
\[ P = \text{constant} \]
This means that the product of force and velocity remains constant as the automobile moves.

3. **Analyzing the Relationship**:
From the equation \( P = F \cdot v \), if power is constant, we can rearrange it to express force in terms of velocity:
\[ F = \frac{P}{v} \]
This shows that the force \( F \) is inversely proportional to the velocity \( v \).

4. **Implications of Inverse Relationship**:
- If the velocity \( v \) increases, the force \( F \) must decrease to keep the power constant.
- Conversely, if the velocity \( v \) decreases, the force \( F \) must increase.

5. **Conclusion**:
Therefore, both the driving force and the velocity cannot be constant simultaneously. As one changes, the other must change to maintain the constant power condition. Hence, the correct conclusion is that the driving force and velocity vary inversely with each other.

### Final Answer:
The driving force and velocity both vary; they cannot be constant when the power is constant.

---